Abstract:
Background to the Debate Only two industrialized countries, the United States and New Zealand, allow direct-to-consumer advertising (DTCA) of prescription medicines, although New Zealand is planning a ban [1]. The challenge for these governments is ensuring that DTCA is more beneficial than harmful. Proponents of DTCA argue that it helps to inform the public about available treatments and stimulates appropriate use of drugs for high-priority illnesses (such as statin use in people with ischemic heart disease). Critics argue that the information in the adverts is often biased and misleading, and that DTCA raises prescribing costs without net evidence of health benefits.

Abstract:
We performed a cross-sectional study of 113 advertisements for antihypertensive drugs from 4 general practice-oriented Australian medical publications in 2004. Advertisements were evaluated using a quality checklist based on a review of hypertension management guidelines. Main outcome measures included: frequency with which antihypertensive classes were advertised, promotion of thiazide class drugs as first line agents, use of statistical claims in advertisements, mention of harms and prices in the advertisements, promotion of assessment and treatment of cardiovascular risk, promotion of lifestyle modification, and targeting of particular patient subgroups.Thiazides were the most frequently advertised drug class (48.7% of advertisements), but were largely promoted in combination preparations. The only thiazide advertised as a single agent was the most expensive, indapamide. No advertisement specifically promoted any thiazide as a better first-line drug. Statistics in the advertisements tended to be expressed in relative rather than absolute terms. Drug costs were often reported, but without cost comparisons between drugs. Adverse effects were usually reported but largely confined to the advertisements' small print. Other than mentioning drug interactions with alcohol and salt, no advertisements promoted lifestyle modification. Few advertisements (2.7%) promoted the assessment of cardiovascular risk.Print advertisements for antihypertensive medications in Australia provide some, but not all, of the key messages required for guideline-concordant care. These results have implications for the regulation of drug advertising and the continuing education of doctors.Hypertension is a major risk factor for cardiovascular disease [1] and the most common single problem managed in Australian general practice. [2] For more than a decade expensive new antihypertensive drugs have been prescribed more frequently than the older and more cost effective thiazide diuretics. [3-6] Newer

Abstract:
Background Pharmaceutical companies spent $57.5 billion on pharmaceutical promotion in the United States in 2004. The industry claims that promotion provides scientific and educational information to physicians. While some evidence indicates that promotion may adversely influence prescribing, physicians hold a wide range of views about pharmaceutical promotion. The objective of this review is to examine the relationship between exposure to information from pharmaceutical companies and the quality, quantity, and cost of physicians' prescribing. Methods and Findings We searched for studies of physicians with prescribing rights who were exposed to information from pharmaceutical companies (promotional or otherwise). Exposures included pharmaceutical sales representative visits, journal advertisements, attendance at pharmaceutical sponsored meetings, mailed information, prescribing software, and participation in sponsored clinical trials. The outcomes measured were quality, quantity, and cost of physicians' prescribing. We searched Medline (1966 to February 2008), International Pharmaceutical Abstracts (1970 to February 2008), Embase (1997 to February 2008), Current Contents (2001 to 2008), and Central (The Cochrane Library Issue 3, 2007) using the search terms developed with an expert librarian. Additionally, we reviewed reference lists and contacted experts and pharmaceutical companies for information. Randomized and observational studies evaluating information from pharmaceutical companies and measures of physicians' prescribing were independently appraised for methodological quality by two authors. Studies were excluded where insufficient study information precluded appraisal. The full text of 255 articles was retrieved from electronic databases (7,185 studies) and other sources (138 studies). Articles were then excluded because they did not fulfil inclusion criteria (179) or quality appraisal criteria (18), leaving 58 included studies with 87 distinct analyses. Data were extracted independently by two authors and a narrative synthesis performed following the MOOSE guidelines. Of the set of studies examining prescribing quality outcomes, five found associations between exposure to pharmaceutical company information and lower quality prescribing, four did not detect an association, and one found associations with lower and higher quality prescribing. 38 included studies found associations between exposure and higher frequency of prescribing and 13 did not detect an association. Five included studies found evidence for association with higher costs, four

Abstract:
In this paper we study symmetry reductions and exact solutions of the shallow water wave (SWW) equation $$u_{xxxt} + \alpha u_x u_{xt} + \beta u_t u_{xx} - u_{xt} - u_{xx} = 0,\eqno(1)$$ where $\alpha$ and $\beta$ are arbitrary, nonzero, constants, which is derivable using the so-called Boussinesq approximation. Two special cases of this equation, or the equivalent nonlocal equation obtained by setting $u_x=U$, have been discussed in the literature. The case $\alpha=2\beta$ was discussed by Ablowitz, Kaup, Newell and Segur [{\it Stud.\ Appl.\ Math.}, {\bf53} (1974) 249], who showed that this case was solvable by inverse scattering through a second order linear problem. This case and the case $\alpha=\beta$ were studied by Hirota and Satsuma [{\it J.\ Phys.\ Soc.\ Japan}, {\bf40} (1976) 611] using Hirota's bi-linear technique. Further the case $\alpha=\beta$ is solvable by inverse scattering through a third order linear problem. In this paper a catalogue of symmetry reductions is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole [{\it J.\ Math.\ Mech.\/}, {\bf 18} (1969) 1025]. The classical Lie method yields symmetry reductions of (1) expressible in terms of the first, third and fifth \p\ transcendents and Weierstrass elliptic functions. The nonclassical method yields a plethora of exact solutions of (1) with $\alpha=\beta$ which possess a rich variety of qualitative behaviours. These solutions all like a two-soliton solution for $t<0$ but differ radically for $t>0$ and may be viewed as a nonlinear superposition of two solitons, one travelling to the left with arbitrary speed and the other to the right with equal and opposite speed.

Abstract:
Classical and nonclassical symmetries of the nonlinear heat equation $$u_t=u_{xx}+f(u),\eqno(1)$$ are considered. The method of differential Gr\"obner bases is used both to find the conditions on $f(u)$ under which symmetries other than the trivial spatial and temporal translational symmetries exist, and to solve the determining equations for the infinitesimals. A catalogue of symmetry reductions is given including some new reductions for the linear heat equation and a catalogue of exact solutions of (1) for cubic $f(u)$ in terms of the roots of $f(u)=0$.

Abstract:
In this paper we study a shallow water equation derivable using the Boussinesq approximation, which includes as two special cases, one equation discussed by Ablowitz et. al. [Stud. Appl. Math., 53 (1974) 249--315] and one by Hirota and Satsuma [J. Phys. Soc. Japan}, 40 (1976) 611--612]. A catalogue of classical and nonclassical symmetry reductions, and a Painleve analysis, are given. Of particular interest are families of solutions found containing a rich variety of qualitative behaviours. Indeed we exhibit and plot a wide variety of solutions all of which look like a two-soliton for t>0 but differ radically for t<0. These families arise as nonclassical symmetry reduction solutions and solutions found using the singular manifold method. This example shows that nonclassical symmetries and the singular manifold method do not, in general, yield the same solution set. We also obtain symmetry reductions of the shallow water equation solvable in terms of solutions of the first, third and fifth Painleve equations. We give evidence that the variety of solutions found which exhibit ``nonlinear superposition'' is not an artefact of the equation being linearisable since the equation is solvable by inverse scattering. These solutions have important implications with regard to the numerical analysis for the shallow water equation we study, which would not be able to distinguish the solutions in an initial value problem since an exponentially small change in the initial conditions can result in completely different qualitative behaviours.

Abstract:
In this article we present first an algorithm for calculating the determining equations associated with so-called ``nonclassical method'' of symmetry reductions (a la Bluman and Cole) for systems of partial differentail equations. This algorithm requires significantly less computation time than that standardly used, and avoids many of the difficulties commonly encountered. The proof of correctness of the algorithm is a simple application of the theory of Grobner bases. In the second part we demonstrate some algorithms which may be used to analyse, and often to solve, the resulting systems of overdetermined nonlinear PDEs. We take as our principal example a generalised Boussinesq equation, which arises in shallow water theory. Although the equation appears to be non-integrable, we obtain an exact ``two-soliton'' solution from a nonclassical reduction.